Κυματοπλατύεδρο
Κυματοπλατύεδρον amplituhedron thumb|300px| [[Φυσική Φυσικοί Γης Επιστημονικοί Κλάδοι Φυσικής Νόμοι Φυσικής Θεωρίες Φυσικής Πειράματα Φυσικής Παράδοξα Φυσικής ]] thumb|300px|[[Κύμα.]] thumb|300px|[[Κύμα.]] - Γεωμετρικό Δόμημα. Ετυμολογία Η ονομασία "Κυματοπλατύεδρον" σχετίζεται ετυμολογικά με την λέξη "έδρα". Εισαγωγή An amplituhedron is a geometric structure discovered in 2013 that underlies simplified calculation of particle interactions in some quantum field theories. In planar N = 4 supersymmetric Yang–Mills theory an amplituhedron is defined within a mathematical space known as the Positive Grassmannian. Amplituhedron theory challenges the notion that space-time locality and unitarity are necessary components of a model of particle interactions. Instead, they are properties that emerge from an underlying phenomenon. The research in this area has been led by Nima Arkani-Hamed. The physicist Edward Witten described the work as “very unexpected" and said that "it is difficult to guess what will happen or what the lessons will turn out to be." Description In the approach, on-shell scattering processes are described by a positive Grassmanian, a structure in algebraic geometry that generalizes the idea of a simplex in projective space. A simplex is a polytope, a kind of higher dimensional polyhedron, and the values being calculated are scattering amplitudes, and so the object is called an amplituhedron. Using Twistor theory, BCFW recursion relations involved in the scattering process may be represented as a small number of Twistor diagrams. These diagrams effectively provide the recipe for constructing the positive Grassmannian, i.e. the amplituhedron, which may be captured in a single equation. When the volume of the amplituhedron is calculated in the planar limit of [[N=4_super_Yang-Mills |''N'' = 4 D'' = 4 supersymmetric Yang–Mills theory]], it describes the scattering amplitudes of subatomic particles. The amplituhedron thus provides a more intuitive geometric model for calculations whose underlying principles were until then highly abstract.4 gravitons and a grad student; The Amplituhedron and Other Excellently Silly Words Implications The twistor approach simplifies the calculations of particle interactions. In a perturbative approach to quantum field theory, such interactions may require the calculation of hundreds of Feynman diagrams. In contrast, twistor theory provides an approach in which scattering amplitudes can be computed in a way that yields much simpler expressions. The twistor approach has previously been relatively abstract. The amplituhedron provides an underlying model for the first time. Its geometric nature suggests the possibility that the nature of the universe, both classical relativistic spacetime and quantum mechanics, can also be described with geometry. Calculations can be done without assuming the quantum mechanical properties of locality and unitarity, which could aid the investigation of theories of quantum gravity. Since the planar limit of the ''N = 4 supersymmetric Yang–Mills theory is a toy theory that does not describe the real world, the relevance of this technique for more realistic quantum field theories is currently unknown, but it provides promising directions for research into theories about the real world. Υποσημειώσεις Εσωτερική Αρθρογραφία * Grassmannian * Twistor space * Wilson loop Βιβλιογραφία * Arkani-Hameda, Bourjailyb, Cachazoc, Goncharovd, Postnikove and Trnka, Scattering Amplitudes and the Positive Grassmannian, Arxiv paper 1212.5605 (Dec 2012)http://arxiv.org/abs/1212.5605 * * , Subramanyan Chandrasekhar Lecture, 25 September 2012. * [http://ncatlab.org/nlab/show/N%3D4+D%3D4+super+Yang-Mills+theory N'' = 4 ''D = 4 super Yang–Mills theory] from nLab * Arxiv paper on Total positivity, Grassmannians, and networks (Sept 2006) * 4 gravitons and a grad student; The Amplituhedron and Other Excellently Silly Words Ιστογραφία *Ομώνυμο άρθρο στην Βικιπαίδεια *Ομώνυμο άρθρο στην Livepedia *[ ] *[ ]